The Zagreb Eccentric Vertex Degree Indices of Nanotubes and Nanotori

Abstract

The eccentric vertex degree of a vertex v of a simple connected graph G, e(v), is defined as: max{d(u1),d(u2,) ..., d(un)}, where d(ui) denotes the degree of the vertex of u(i) which is one of the furthest vertices from v. The total eccentric vertex degree is defined as: TE = Sigma()ev)(v is an element of E(G), where e(v) denotes the eccentric degree of the vertex v. The first Zagreb eccentric vertex degree alpha index is defined as: DM1 alpha = Sigma(ev2)(v is an element of E(G)). The first Zagreb eccentric vertex degree beta index is defined as: DM1 beta = Sigma((eu + ev))(uv is an element of E(G)). And the second Zagreb eccentric vertex degree index is defined as: DM2 = Sigma(euev)(uv is an element of E(G)). In this study, we compute the exact value of the Zagreb eccentric vertex degree indices of TUC4C8(S) nanotubes and TC4C8(S) nanotori.